膨胀土应力松弛的分数阶模型
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摘要
为了更准确地描述膨胀土应力松弛的力学特性,应用分数阶微积分理论构造的软体元件取代传统元件模型中的理想黏滞元件,并考虑黏滞系数的损伤劣化,建立了可以更加准确地反映南宁膨胀土非线性应力松弛特性的三元件模型。通过一系列室内试验研究,探索了在不同含水率条件下南宁膨胀土的应力松弛规律,并根据对试验结果的分析,确定了相关的模型参数,得到了膨胀土在不同含水率条件下的应力松弛方程。与整数阶西原模型和整数阶St.Venant模型进行对比,其结果表明所提出的改进模型能更有效地模拟膨胀土应力松弛的全过程,且模型具有结构简单、计算参数少、计算精度高和便于实际应用等优点。研究结果为膨胀土在长期荷载作用下的应力松弛分析提供了理论基础。
To accurately describe the mechanical behavior of stress relaxation of expansive soils, the software element is constructed by applying the theory of fractional calculus to replace the ideal viscous element in the traditional element model. The damage degradation of viscosity coefficient is considered. A new three-element model is established to better reflect the nonlinear stress relaxation behaviors of Nanning expansive soils. The stress relaxation of Nanning expansive soil under different water contents is studied by a series of indoor tests. The relevant model parameters and stress relaxation equations are determined according to the analysis of the tested results. By comparing the proposed model with the traditional integer order models(such as the traditional St.Venant model and Nishihara model), the results show that the proposed model can more effectively simulate the whole process of the stress relaxation of the expansive soils. Furthermore, the proposed model has advantages on simple structure, few calculation parameters, high accuracy, easy to practical application. The research results provide a theoretical basis for the analysis of the stress relaxation of expansive soils under long term load.
To accurately describe the mechanical behavior of stress relaxation of expansive soils, the software element is constructed by applying the theory of fractional calculus to replace the ideal viscous element in the traditional element model. The damage degradation of viscosity coefficient is considered. A new three-element model is established to better reflect the nonlinear stress relaxation behaviors of Nanning expansive soils. The stress relaxation of Nanning expansive soil under different water contents is studied by a series of indoor tests. The relevant model parameters and stress relaxation equations are determined according to the analysis of the tested results. By comparing the proposed model with the traditional integer order models(such as the traditional St.Venant model and Nishihara model), the results show that the proposed model can more effectively simulate the whole process of the stress relaxation of the expansive soils. Furthermore, the proposed model has advantages on simple structure, few calculation parameters, high accuracy, easy to practical application. The research results provide a theoretical basis for the analysis of the stress relaxation of expansive soils under long term load.
引文
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[13]李珍玉,肖宏彬,金文婷,等.南宁膨胀土非线性流变模型研究[J].岩土力学,2012,33(8):2297-2302.LI Zhen-yu,XIAO Hong-bin,JIN Wen-ting,et al.Study of nonlinear rheological model of Nanning expansive soils[J].Rock and Soil Mechanics,2012,33(8):2297-2302.
[14]贺聪,肖宏彬,周伟,等.南宁膨胀土非线性剪切应力松弛特性试验[J].岩土力学,2013,34(1):22-27.HE Cong,XIAO Hong-bin,ZHOU Wei,et al.Experimental study on nonlinear shear stress relaxation characteristics of expansive soil in Nanning[J].Rock and Soil Mechanics,2013,34(1):22-27.
[15]沈珠江.结构性黏土的弹塑性损伤模型[J].岩土工程学报,1993,15(3):21-28.SHEN Zhu-jiang.An elasto-plastic damage model for cemented clays[J].Chinese Journal of Geotechnical Engineering,1993,15(3):21-28.
[16]YANG PAN,LAM YEECHEONG,ZHU KEQIN.Constitutive equation with fractional derivatives for the generalized UCM model[J].Journal of Non-Newtonian Fluid Mechanics,2010,165:88-97.
[2]张为民.一种采用分数阶导数的新流变模型理论[J].湘潭大学学报(自然科学),2001,23(1):30-35.ZHANG Wei-min.A new rheological model theory with fractional order derivatives[J].Journal of Xiangtan University(Natural Science),2001,23(1):30-35.
[3]孙海忠,张卫.一种分析软土黏弹性的分数导数开尔文模型[J].岩土力学,2007,28(9):1983-1986.SUN Hai-zhong,ZHANG Wei.Analysis of soft soil with viscoelastic fractional derivative Kelvin model[J].Rock and Soil Mechanics,2007,28(9):1983-1986.
[4]殷德顺,任俊娟,和成亮,等.一种新的岩土流变模型元件[J].岩石力学与工程学报,2007,26(9):1989-1903.YIN De-shun,REN Jun-juan,HE Cheng-liang,et al.A new rheological model element for geomaterials[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(9):1989-1903.
[5]郭佳奇,乔春生,徐冲,等.基于分数阶微积分的KelvinVoigt流变模型[J].中国铁道科学,2009,30(4):1-5.GUO Jia-qi,QIAO Chun-sheng,XU Chong,et al.The Kelvin-Voigt rheological model based on fractional calculus[J].China Railway Science,2009,30(4):1-5.
[6]何利军,孔令伟,吴文军,等.采用分数阶导数描述软黏土蠕变的模型[J].岩土力学,2011,32(2):239-243.HE Li-jun,KONG Ling-wei,WU Wen-jun,et al.A description of creep model for soft soil with fractional derivative[J].Rock and Soil Mechanics,2011,32(2):239-243.
[7]段晓梦,殷德顺,李彦青,等.基于分数阶微积分的岩土材料变形研究[J].河海大学学报(自然科学版),2013,42(2):145-149.DUAN Xiao-meng,YIN De-shun,LI Yan-qing,et al.Study on deformation of geomaterials based on fractional order calculus[J].Journal of Hohai University(Natural Sciences),2013,42(2):145-149.
[8]何明明,李宁,朱才辉,等.岩石分数阶体积变形模型及其试验研究[J].岩土力学,2016,37(11):3137-3144.HE Ming-ming,LI Ning,ZHU Cai-hui,et al.The volume deformation behavior of rock based on fractional calculus and its experimental study[J].Rock and Soil Mechanics,2016,37(11):3137-3144.
[9]唐皓,赵法锁,段钊,等.基于分数阶微积分改进的黄土西原模型[J].水文地质工程地质,2014,41(5):50-56.TANG Hao,ZHAO Fa-suo,DUAN Zhao,et al.The improved Nishihara model of loess based on fractional calculus[J].Hydrogeology&Engineering Geology,2014,41(5):50-56.
[10]徐国文,何川,胡雄玉,等.基于分数阶微积分的改进西原模型及其参数智能辨识[J].岩土力学,2015,36(2):132-138.XU Guo-wen,HE Chuan,HU Xiong-yu,et al.A modified Nishihara model based on fractional calculus theory and its parameter intelligent identification[J].Rock and Soil Mechanics,2015,36(2):132-138.
[11]何志磊,朱珍德,朱明礼,等.基于分数阶导数的非定常蠕变本构模型研究[J].岩土力学,2016,37(3):737-775.HE Zhi-lei,ZHU Zhen-de,ZHU Ming-li,et al.An unsteady creep constitutive model based on fractional order derivatives[J].Rock and Soil Mechanics,2016,37(3):737-775.
[12]金文婷,肖宏彬.南宁膨胀土剪切蠕变特性及流变模型研究[J].公路工程,2011,36(6):64-69,77.JIN Wen-ting,XIAO Hong-bin.Experimental study on shear creep characteristic and rheological model of Nanning expansive soils[J].Highway Engineering,2011,36(6):64-69,77.
[13]李珍玉,肖宏彬,金文婷,等.南宁膨胀土非线性流变模型研究[J].岩土力学,2012,33(8):2297-2302.LI Zhen-yu,XIAO Hong-bin,JIN Wen-ting,et al.Study of nonlinear rheological model of Nanning expansive soils[J].Rock and Soil Mechanics,2012,33(8):2297-2302.
[14]贺聪,肖宏彬,周伟,等.南宁膨胀土非线性剪切应力松弛特性试验[J].岩土力学,2013,34(1):22-27.HE Cong,XIAO Hong-bin,ZHOU Wei,et al.Experimental study on nonlinear shear stress relaxation characteristics of expansive soil in Nanning[J].Rock and Soil Mechanics,2013,34(1):22-27.
[15]沈珠江.结构性黏土的弹塑性损伤模型[J].岩土工程学报,1993,15(3):21-28.SHEN Zhu-jiang.An elasto-plastic damage model for cemented clays[J].Chinese Journal of Geotechnical Engineering,1993,15(3):21-28.
[16]YANG PAN,LAM YEECHEONG,ZHU KEQIN.Constitutive equation with fractional derivatives for the generalized UCM model[J].Journal of Non-Newtonian Fluid Mechanics,2010,165:88-97.